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We formulate the ``tensor-optimized high-momentum antisymmetrized molecular dynamics'' (TO-HMAMD) framework for ab initio calculations of nuclei by hybridizing the tensor-optimized (TO) and high-momentum (HM) AMD approaches. This hybrid approach has advantages in both analytical simplicity and numerical efficiency compared with other AMD-based methods which treat the bare interaction, especially for heavier nuclear systems. In this work, the $s$-shell nucleus $^{4}\mathrm{He}$ is calculated with TO-HMAMD by including up to double product of nucleon-nucleon ($NN$) correlations, described by using high-momentum pairs and spatial correlation functions of nucleons. The total energy and radius of the $^{4}\mathrm{He}$ nucleus are well reproduced using the $\mathrm{AV}{8}^{\ensuremath{'}}$ interaction. The spin-isospin channel dependence is also discussed for $NN$ correlations, which are found to be mostly contributed in the even-state channels, especially the triplet-even channel. Analyses of the analytical formation and numerical results suggest that TO-HMAMD could be a promising framework for $p$-shell nuclear systems.

Linear-chain and gas-like structures have been investigated in nuclei near 12C by using antisymmetrized molecular dynamics combined with generator coordinate method. We found that linear-chain structures and gas-like structures of three clusters exist quite universally. 10Be, 11B, and 12C have gas-like states of 2α+dineutron, 2α+t, and 3α structures, respectively. There are linear-chain states, in which 2α clusters are formed and valence nucleons occupy the σ-orbit. In neutron-rich C isotopes, linear-chain structures of three α clusters surrounded by excess neutrons appear. Excess neutrons stabilize the linear chain structures, and therefore, linear-chain states appear below the 3α+Xn threshold energy. In 14C, candidates of the linear-chain states are observed in recent 10Be+α resonant scattering experiments.Linear-chain and gas-like structures have been investigated in nuclei near 12C by using antisymmetrized molecular dynamics combined with generator coordinate method. We found that linear-chain structures and gas-like structures of three clusters exist quite universally. 10Be, 11B, and 12C have gas-like states of 2α+dineutron, 2α+t, and 3α structures, respectively. There are linear-chain states, in which 2α clusters are formed and valence nucleons occupy the σ-orbit. In neutron-rich C isotopes, linear-chain structures of three α clusters surrounded by excess neutrons appear. Excess neutrons stabilize the linear chain structures, and therefore, linear-chain states appear below the 3α+Xn threshold energy. In 14C, candidates of the linear-chain states are observed in recent 10Be+α resonant scattering experiments.

We developed a new variational method of tensor-optimized antisymmetrized molecular dynamics (TOAMD) to treat the bare interactions for finite nuclei. In TOAMD, two kinds of the correlation functions for tensor force and short-range repulsion are multiplied to the AMD wave function successively in the power series form. Each correlation function in every correlation term is independently optimized in the total energy variation. We show the results of TOAMD for s-shell nuclei using bare AV8’ NN potential. The binding energy and the Hamiltonian components nicely reproduce the values of the few-body calculations. The energies obtained in TOAMD are shown to be lower than those of the variational Monte Carlo method based on the Jastrow’s product-type correlation functions. This means that the power series expansion using the independent correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method. We further extended TOAMD by adopting the multi-configuration of the AMD wave functions, which include the high-momentum (HM) components of nucleon motions. This framework is called high-momentum TOAMD (HM-TOAMD) and we show the results of HM-TOAMD for s-shell nuclei.We developed a new variational method of tensor-optimized antisymmetrized molecular dynamics (TOAMD) to treat the bare interactions for finite nuclei. In TOAMD, two kinds of the correlation functions for tensor force and short-range repulsion are multiplied to the AMD wave function successively in the power series form. Each correlation function in every correlation term is independently optimized in the total energy variation. We show the results of TOAMD for s-shell nuclei using bare AV8’ NN potential. The binding energy and the Hamiltonian components nicely reproduce the values of the few-body calculations. The energies obtained in TOAMD are shown to be lower than those of the variational Monte Carlo method based on the Jastrow’s product-type correlation functions. This means that the power series expansion using the independent correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method. We further extended TOAMD by adopting the multi-configuration of the AMD wave fu...

We recently proposed a new variational theory of "tensor-optimized antisymmetrized molecular dynamics" (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8$^\prime$ for $s$-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of $s$-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions., 25 pages, 24 figures, corrected typos

Tensor-optimized antisymmetrized molecular dynamics (TOAMD) is the basis of the successive variational method for nuclear many-body problem. We apply TOAMD to finite nuclei to be described by the central interaction with strong short-range repulsion, and compare the results with the unitary correlation operator method (UCOM). In TOAMD, the pair-type correlation functions and their multiple products are operated to the AMD wave function. We show the results of TOAMD using the Malfliet-Tjon central potential containing the strong short-range repulsion. Adding the double products of the correlation functions in TOAMD, the binding energies are converged quickly to the exact values of the few-body calculations for s-shell nuclei. This indicates the high efficiency of TOAMD for treating the short-range repulsion in nuclei. We also employ the s-wave configurations of nuclei with the central part of UCOM, which reduces the short-range relative amplitudes of nucleon pair in nuclei to avoid the short-range repulsion. In UCOM, we further perform the superposition of the s-wave configurations with various size parameters, which provides a satisfactory solution of energies close to the exact and TOAMD values., Comment: 8 pages, 9 figures

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon-nucleon interaction AV8'. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions., Comment: 7 pages, 5 figures, added references, corrected typos

Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call "HM-TOAMD". In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon-nucleon interaction AV8', we sufficiently reproduce the energy and radius of the 3H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method., Comment: 9 pages, 5 figures, 1 table, Accepted by PTEP

We developed a new variational method for tensor-optimized antisymmetrized molecular dynamics (TOAMD) for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion are introduced and used in the power series form of the wave function, which is different from the Jastrow method. Here, nucleon pairs are correlated in multi-steps with different forms, while they are correlated only once including all pairs in the Jastrow correlation method. Each correlation function in every term is independently optimized in the variation of total energy in TOAMD. For $s$-shell nuclei using the nucleon-nucleon interaction, the energies in TOAMD are better than those in the variational Monte Carlo method with the Jastrow correlation function. This means that the power series expansion using the correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method., Comment: 7 pages, 4 figures. arXiv admin note: text overlap with arXiv:1706.09560, update references

Structures of excited states in 11B are investigated with a method of β – γ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various cluster structures are suggested in excited states. For negative-parity states, we suggest a band with a 2α + t cluster structure. This band starts from the \({3/2^{-}_{3}}\) state and can correspond to the experimental band observed recently. We find that the feature of the \({3/2^{-}_{3}}\) is quite similar to the \({0^{+}_{2}}\) state in 12C.

Spatial correlations of spin-zero neutron pairs in 6 He and 8 He are investigated by analyzing two-neutron density of microscopic wave functions obtained by antisymmetrized molecular dynamics (AMD). Results suggest dineutron correlations at the surface of these neutron-rich He isotopes. The dineutron correlations are weaker in the ground state of 8 He than in 6 He but again pronounced in the excited [Formula: see text] of 8 He .

We propose a new method of the $��$-$��$ constraint for quadrupole deformation in antisymmetrized molecular dynamics (AMD) to describe various cluster and shell-model structures in the ground and excited states of light nuclei. We apply this method to N=6 isotones, $^{10}$Be, $^{12}$C, $^{9}$Li, and $^{11}$B, and find various structures as functions of the deformation parameters, $��$ and $��$. In these nuclei, shell-model-like structures appear in the small $��$ region, while cluster structures develop well in the large $��$ region where various geometric configurations of clusters are obtained depending on the $��$ parameter. For $^{10}$Be and $^{12}$C, we superpose the basis AMD wave functions obtained by the $��$-$��$ constraint method to calculate energy spectra, and prove the advantages of the present method of the two-dimensional $��$-$��$ constraint in the framework of AMD., 23pages, 14 figures

Structure of excited states in 14 C were investigated with a method of the antisymmetrized molecular dynamics model. Variation with constraints on the quadrupole deformations (β, γ) was performed, and the configurations were superposed within the AMD framework. Above the ground band, three excited bands with the developed 3α-cluster core structures were suggested. Characteristic structures such as a triaxial structure and a linear-chain structure appear in the excited bands. It was found that the 10 Be correlation exists in the linear-chain structure.

We report three-center cluster structures in the excited states of 11 B (11 C ), 8 He and 14 C based on theoretical calculations with the antisymmetrized molecular dynamics (AMD). In particular we discuss the cluster gas-like states 2α + t(2α+3 He ) in 11 B (11 C ) and α + 2n + 2n in 8 He . In 14 C , the 3α linear-chain structure is discussed.

We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments are confirming this prediction as the change of the proton radii. Behind this enhancement and reduction of the clustering, there are underlying shell effects called molecular- and atomic-orbits. These orbits form covalent and ionic bonding of the clusters analogous to the atomic molecules. It was found that this "molecular-orbit picture" reasonably explains the low-lying spectra of Be isotopes. The molecular-orbit picture is extended to other systems having parity asymmetric cluster cores and to the three cluster systems. O and Ne isotopes are the candidates of the former, while the $3\alpha$ linear chains in C isotopes are the latter. For both subjects, many intensive studies are now in progress. We also pay a special attention to the observables which are the fingerprint of the clustering. In particular, we focus on the monopole and dipole transitions which are recently regarded as good probe for the clustering. We discuss how they have and will reveal the exotic clustering., Comment: 96 pages, 44 figures

We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in strongly interacting system. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model (TOSM). We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".

We propose a new method of the β-γ constraint for quadrupole deformation in antisymmetrized molecular dynamics (AMD) to describe various cluster and shell-model structures in the ground and excited states of light nuclei. To check its applicability, we apply this method to N = 6 isotones, 10 Be , 12 C , 9 Li , and 11 B , and find various shell-model and cluster structures as functions of the deformation parameters, β and γ. We also investigate 14 C with the β-γ constraint AMD. For positive-parity states, above the ground band, three excited bands with the developed 3α-cluster core structures are suggested. Characteristic structures such as a triaxial structure and a linear-chain structure having 10 Be +α correlation appear in the excited bands.

In this paper, we discuss cluster phenomena in light nuclei based on calcula- tions using the antisymmetrized molecular dynamics (AMD) method. Cluster structures in C, B, and Be were studied systematically, and their cluster formation and excitation are discussed. Cluster gas states and their band members are suggested for the excited states of 12 C and 11 B. The ground state cluster correlation and excited cluster gas state are discussed from the point of view of symmetry breaking and restoration.

Structures of ground and excited states of C isotopes are theoretically investigated with the method of antisymmetrized molecular dynamics. For 14C, it is suggested that a linear-chain 3a structure can be stabilized by the excess neutrons and may construct an rotational band near the 10Be+α threshold energy. In 11C and its mirror nucleus 11B, a cluster gas state and a linear-like cluster state are suggested in excited states. Possible assignment of the cluster states in 11B with the experimental energy levels are discussed. Deformations of proton and neutron densities of the ground bands in neutron-rich C are also discussed.

The cluster structure of excited states in 11B is investigated with a method of β-γ constrained antisymmetrized molecular dynamics in combination with the generator coordinate method. For negative-parity states, we identify a band with a 2α+t cluster structure. This band starts from the 3/2−3 state and may correspond to the experimental band observed recently. We find that the composision of the 3/2−3 state s quite similar to that of the 0+2 state in 12C.